A modern award is a legal document that covers an employees conditions for employment. This covers various things such as; pay rates (as above), penalty rates (working weekends, night shift, public holidays, etc.), hours of work (38 hours a week), breaks (tea breaks, lunch breaks), rosters, and overtime.

There are quite a few awards which you can find here: https://www.fairwork.gov.au/employment-conditions/awards/list-of-awards

I don't believe Australia has ever had tipped minimum wage (and it should never).

But that is just a minimum standard, can't you negotiate for a higher salary? Yes

An employee can negotiate with their employer for better conditions of employment, which is covered as an employment contract. (Should be noted, an employment contract cannot leave the employee worse off, ie. cannot erode your rights under an award).

More information here: https://www.fairwork.gov.au/employment-conditions/awards